2014/05/31 by Alexander V. Turbiner, J. C. López Vieyra, Juan Carlos Lopez Vieyra · 9 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Physical and Chemical Molecular Interactions #Algorithm #Arithmetic #Atomic and Molecular Physics #Atomic number #Atomic physics #Charge (physics) #Consistency (knowledge bases) #Coulomb #Decimal #Discrete mathematics #Electron #Energy (signal processing) #Ground state #Ion #Mathematics #Physics #Quantum mechanics #State (computer science) #physics.atom-ph #quant-ph
paper · pdf · doi:10.1139/cjp-2015-0366
published in Canadian Journal of Physics 94(3), 249-253 (NRC Research Press) · 11 pages, 2 Tables; the title is slightly modified, the text is essentially rewritten, the emphasis to a relation of presented results to the Kato theorem is given, one Table is removed, new references are added, main conclusions remain unchanged, submitted to Can J Physics
arxiv created 2015/06/02 · openalex publication_date 2015/11/17 · openalex created_date 2016/06/24 · arxiv updated 2016/06/30 · openalex updated_date 2026/08/05
The 1/Z expansion for the ground state energy of the Coulomb system of an infinitely massive center of charge Z and two electrons (two-electron ionic sequence) is studied. A critical analysis of the 1/Z coefficients presented in Baker et al. (Phys. Rev. A, 41, 1247 (1990)) is performed and its numerical deficiency is indicated, leading, in particular, to unreliable decimal digits beyond digits 11–12 of the first coefficients. We made a consistency check of the 1/Z-expansion with accurate energies for Z = 1–10: the weighted partial sums of the 1/Z expansion with Baker et al. coefficients reproduce systematically the ground state energies of two-electron ions with Z ≥ 2 up to 12 decimal digits and for Z = 1 up to 10 decimal digits calculated by Nakashima and Nakatsuji (J. Chem. Phys. 127, 224104 (2007)) with unprecedented accuracy. This rules out the presence of non-analytic terms at Z = ∞ contributing to the first 10–12 decimal digits in the ground state energy; it agrees with the Kato theorem about convergence of the 1/Z expansion within that accuracy. The ground state energy of two-electron ions Z = 11 (Na 9+ ) and Z = 12 (Mg 10+ ) is calculated with 12 decimal digits. This study can be considered as the independent confirmation of the correctness of 10 decimal digits in all 401 coefficients of 1/Z-expansion printed in Baker et al. (Phys. Rev. A, 41, 1247 (1990)).